Gas sensor and method for determining a concentration of gas in a two-component mixture

ABSTRACT

The described sensor allows determination of the concentration of a gas in a two-component mixture at variable pressure by measuring the diffusivity and the thermal conductivity. The sensor is provided to alternately heat the membrane ( 12 ) of a thermally conductive cell ( 1 ) and allow it to cool such that the temperature T M  of the membrane passes from a first stable value to a second stable value and vice versa via a transient mode. The cell produces a signal representative of the temperature T M  of the membrane and the sensor extracts from the signal a first and a second parameter that respectively relate to said first stable value and said transient mode of the signal. A value of the concentration of said gas and of the pressure of said two-mixture is calculated from these two parameters.

The present invention relates to the field of thermal gas sensors. More specifically, it relates to a thermal gas sensor for determining a concentration of gas in a two-component mixture at variable pressure. It also relates to a method for determining a concentration of gas in a two-component mixture of variable concentration.

Thermal gas sensors take advantage of thermal conductivity properties of the gases to provide information on the nature of a gas or its concentration in a gaseous mixture. The thermal conductivity X of a gas is its capacity to transport heat under the effect of a temperature gradient. It is an intrinsic magnitude of a gas at a given pressure and temperature and this is why its measurement is able to provide an indication of the composition of a gaseous mixture. Thermal gas sensors are used in particular for measuring the concentration of hydrogen (H₂) in another gas such as oxygen (O₂), nitrogen (N₂), argon (Ar), carbon dioxide (CO₂) or even air (assuming that it is of fixed composition), since hydrogen differs greatly from other gases because of its high thermal conductivity in comparison to that of heavier molecules. The following values are given for information purposes:

λ_(hydrogen)=0.84 Wm⁻¹K⁻¹

λ_(air)=0.012 Wm⁻¹K^(−1.)

Thermal gas sensors generally have an electrically insulating membrane of low thermal inertia, on which devices for heating the membrane and devices for measuring its temperature are arranged. The membrane is conventionally formed from a thin layer of silicon oxide or nitride deposited onto a silicon substrate, which is locally etched to the rear face of the membrane such that a gas flux can circulate on either side thereof. The heating devices and devices for measuring the temperature respectively comprise a first and a second electrical resistance formed by metal lines meandering over the front face of the membrane. The metal used for the temperature measuring devices has a variable resistance as a function of the temperature, such that measuring the voltage at its terminals enables the temperature of the membrane to be determined. When this latter is heated by the heating devices, its temperature rests at a stable value that is dependent on the thermal conductivity of the gaseous mixture or the ambient gas. As a result of this, the measurement of the temperature of the membrane provides an indication of the nature of the ambient gas or of the composition of the gaseous mixture. Reference is made to DE4228484 for more details on the structure and operation of such a gas sensor.

A gas sensor of the type described above allows measurement of a variable of a two-component gaseous mixture, i.e. the concentration of one of the gases, on the basis of one parameter: the temperature of a membrane in physical contact with said mixture. It assists in particular in determining the concentration of hydrogen in another gas, as explained above. There is considerable interest in determining the proportion of hydrogen in another gas with precision, since what is at stake in this case concerns the level of safety of installations and personnel. In fact, it is known that hydrogen forms a highly explosive mixture with oxygen, even at low concentrations. The same applies with air, which contains approximately twenty per cent oxygen. A thermal gas sensor provides such an indication at low cost and space requirement, hence its significant technical interest.

However, the measurement of a variable of a two-component gaseous mixture, in the case in point the concentration of one of the gases, on the basis of one parameter: the temperature of a membrane of low thermal inertia, is only possible if all the other variables of the mixture are constant. In particular, the pressure of the gaseous mixture has a significant influence on its conductivity. At variable pressure, it becomes impossible to determine the concentration of a gas in a two-component mixture on the basis of a single temperature measurement of the membrane.

Such a situation is encountered, for example, within an electrolyser unit. These devices are intended in particular for the production of gaseous hydrogen from water. These are currently the subject of significant developments since they offer a clean energy alternative to fossil fuels. Application EP 2 048 759, for example, describes a domestic installation for the production and storage of gaseous hydrogen using an electrolyser supplied with power by a photovoltaic installation. The hydrogen is then used as fuel in a fuel cell fitted, for example, in an electric vehicle.

In an electrolyser of the type described in application EP 2 048 759 hydrogen is produced from liquid water by means of an anode and a cathode. In a variant, the electrolyser is formed by an assembly of electrolytic cells, each of which having an anode and a cathode. Such a device is described in the patent document GB 1,145,751. Whatever the structure of the electrolyser, hydrogen is produced on the cathode side, while oxygen is produced on the anode side. The accumulation of these gases during the production process, respectively on the cathode side and anode side, causes the pressure within the electrolyser to increase progressively up to a value in the order of ten to several tens of bars. Because of the risks of explosion of an oxygen-hydrogen mixture, it is necessary to detect any presence of hydrogen in the oxygen and vice versa over the entire operating pressure range of the electrolyser. To achieve this and because of the above-mentioned limitation of thermal gas sensors, a pressure sensor is generally added to the gas sensor installed in the electrolyser. It is then possible to combine pressure and temperature measurements to get up to the concentration of gas to be determined. However, this solution increases the cost of this type of detection significantly, which represents a major disadvantage for a domestic installation.

The aim of the present invention is to remedy this disadvantage by proposing a thermal gas sensor that is able to determine the concentration of a gas in a two-component mixture at variable pressure. More specifically, the present invention relates to a sensor for determining the concentration of a gas in a two-component mixture at variable pressure according to the attached claim 1.

Because of its features and in particular, as described, the choice of frequency f of the current source supplying the heating devices, the gas sensor according to the invention allows measurement not of one single parameter of the gaseous mixture, i.e. a stable temperature in continuous mode, but two parameters of the gaseous system, one associated with its statics and the other associated with its dynamics. These two parameters inserted into a mathematical function established for this purpose allow determination of not one variable of the gaseous mixture, but two, e.g. the concentration of one of the gases and the pressure of the mixture. Measurement of the pressure of the gaseous mixture by an independent device attached to the gas sensor becomes superfluous.

The present invention also relates to a method for determining the concentration of a gas in a two-component mixture at variable pressure by means of a gas sensor comprising a step of measuring a first characteristic parameter of the conduction of the two-component mixture, a step of measuring a second characteristic parameter of the diffusivity of the two-component mixture and a step of calculating a value of the concentration of said gas and the pressure of said two-component mixture from said parameters with the assistance of a previously established mathematical function and characteristic coefficients of the sensor.

Other features and advantages of the present invention will become evident upon reading the following description provided solely by way of example with reference to the attached drawings:

FIG. 1 is a sectional view of the measurement cell of a gas sensor according to the invention; and

FIG. 2 shows a basic operational diagram of the sensor according to the invention; and

FIG. 3 shows an example of a measurement signal of said sensor.

As an initial observation, it is mentioned that the gas sensor according to the invention is intended in particular to measure hydrogen in oxygen for the reasons outlined above. However, its operating principle for determining variables of a gaseous mixture can be extended to any two-component mixture. Furthermore one of the two gases can be air, assuming that its composition is constant. In the following description it will be noted that % H and % O are respectively the proportions of hydrogen and oxygen forming the two-component mixture to be analysed and P is its pressure, and there will be no further reference to another gas.

The thermal gas sensor according to the invention conventionally comprises a measurement cell intended to be immersed into two-component oxygen/hydrogen mixture to be analysed, shown schematically in FIG. 1 and given the overall reference 1. The cell 1 comprises a rigid base 10 that has an opening 11 in its centre and is covered by an electrically and thermally insulating membrane 12 of low thermal inertia. The opening 11 allows an ambient gas to circulate and transport heat on either side of the membrane 12. The effect of the conductivity of the gas on the temperature of the membrane 12 thus outweighs the cooling associated with other physical phenomena such as heat radiation or conduction through the base 10. Heating devices 13 are arranged on the membrane 12 at the level of the opening 11, while measuring devices 14 for the temperature T_(M) of the membrane 12 are situated in the vicinity of the heating devices 13. Measuring devices 15 for the ambient temperature T_(A) are arranged spaced from the heating devices 13 so as not to be subjected to their effect.

In a particularly advantageous embodiment the cell 1 is made from a sheet of silicon forming the rigid base 10 using production techniques for micromechanical devices well known to the person skilled in the art. The membrane 12 is formed from a layer of silicon nitride Si₃N₄ or silicon oxide SiO₂ deposited on the sheet of silicon or obtained by thermal nitridation or oxidation. Its thickness is typically several hundreds of nanometres. The opening 11 is generally formed by chemical etching of the silicon sheet from its rear face after formation of the membrane 12. The heating devices 13 as well as the measuring devices 14 for the temperature T_(M) of the membrane 12 are formed by metal lines meandering over the membrane 12 above the opening 11. The metal used to form the measuring devices 14 has a resistance R_(M) that varies as a function of temperature in the known manner at a standard reference pressure. The relation linking the resistance R_(M) to the temperature T_(M) of the membrane 12 that is well known to the person skilled to the art has the following form:

R _(M) =R ₀*(1+αT _(M))  (1)

in which the coefficient α is a characteristic of the metal forming the metal line 14: generally platinum, nickel or an alloy of these two metals. In the same way, the measuring devices 15 for the ambient temperature T_(A) are formed from lines of metal, the resistance R_(A) of which is thermo-variable. In a similar manner, the ambient temperature T_(A) is associated with the value of the resistance R_(A) by relation (1). A passivation layer 16 formed from a silicon oxide SiO₂ or a silicon nitride Si₃N₄ covers the metal lines 14 and 15.

The cell 1 is powered by an alternating current source 20 shown schematically in FIG. 2 that supplies a square alternating current of frequency f to the heating devices 13. The frequency f lies in the range of between a few hertz and some tens of hertz, depending on the layout and size of the cell 1. Typically, it lies in the order of 20 hertz. It is selected to allow the heating devices 13 to heat and alternately cool the membrane 12 so that its temperature T_(M) passes from a first stable value T_(H) to a second stable value T_(B) and vice versa via transient modes. This aspect of the gas sensor according to the invention will become clearer by looking at FIG. 3. The temperature T_(M) of the membrane 12 is given by the measuring devices 14, which supply an analog signal representative of T_(M), for instance a value of the resistance R_(M) of the metal line forming the measuring devices 14. Moreover, the ambient temperature T_(A) is given by the measuring devices 15, which supply an analog signal representative of T_(A), for instance a value of the resistance R_(A) of the metal line forming the measuring devices 15. It must be noted here that the temperature T_(M) is a function of the ambient temperature T_(A) and of the thermal conductivity λ of the ambient gas, which is itself a function of the ambient temperature T_(A) and of the nature of said gas.

T _(M) =f(T _(A), conductivity (T _(A), gas))  (2)

Consequently, the temperature T_(A) of the membrane 12 must firstly be corrected in the first order of the effect of the ambient temperature T_(A) in order to give information about the conductivity of the ambient gas. For this purpose, it is the ratio R_(M)/R_(A) that is output from the cell 1, then processed by an electronic circuit 30 comprising a analog to digital converter 21, a controller 22, a memory module 23 and a time base 24.

The analog to digital converter 21 arranged at the output of the cell 1 transforms the analog signal R_(M)/R_(A) into a digital signal, which is processed by the controller 22. The ROM memory module 23 (read only memory) connected to the controller 22 stores a plurality of coefficients characteristic of the gas sensor necessary for processing the R_(M)/R_(A) signal. These coefficients will be explained below. The controller 22 is also connected to a time base 24 formed by a crystal and to the alternating current source 20, whose frequency fit controls.

We will now refer to FIG. 3 that shows the development of the temperature T_(M) of the membrane 12, as measured by the resistance R_(M), and that of the supply current 1 for the heating devices 13 as a function of time. When it is heated by the heating devices 13 in the presence of a gaseous mixture of oxygen and hydrogen, the membrane 12 experiences a rise of its temperature T_(M) to a high stable value T_(H) measured by the measuring devices 14. The high value T_(H) is dependent on the thermal conductivity of the surrounding gaseous mixture that transports the heat supplied by the heating devices 13 reasonably easily. When the heating devices 13 cease to heat the membrane 12, this cools to a low stable value T_(B) that is substantially equal to the temperature of the ambient medium. Between the high T_(H) and low T_(B) stable values, the temperature T_(M) of the membrane 12 passes through transient modes t_(HB) and t_(BH) of cooling and reheating respectively, which are principally determined by the thermal diffusivity of the surrounding gaseous mixture.

In contrast to thermal conductivity, which defines the behaviour of a gas in static mode, diffusivity characterises the capacity of the gas to progress from one temperature to another and determines its behaviour in dynamic mode. Like thermal conductivity, the diffusivity of the gaseous mix depends on the nature of the gases, their concentration and the ambient pressure, but in a very different manner. According to the invention, the pieces of information supplied by high stable temperature T_(H) and by the transient cooling mode t_(HB) are combined to determine the composition of the gaseous mixture, whatever its pressure.

In fact, numerous systematic measurements and tests conducted within the framework of the present invention have made it possible to show that the different variables of the gas to be analysed: % H, % O or P, are associated with the value T_(H) and to the cooling gradient pt_(HB) measured during the transient cooling mode t_(HB) by simple mathematical functions, in which the above-mentioned coefficients play a part. It must be noted here that the cooling of the membrane 12 follows an exponential e^(−k/T) law. The cooling t_(HB) gradient pt_(HB) is thus defined by the following function:

pt _(HB) =d/dt(In((T _(H) −T _(B))/(T _(i) −T _(B)))  (3)

in which the points T_(i), three in number, are measured at different intervals during the transient cooling mode t_(HB), for example, at 10, 14 and 18 ms of the point T_(H) in the present case. It will be noted that the choice of the number of points T_(i) and of the time interval separating them depends on the layout of the cell 1 as well as numerous other parameters such as the nature of the gases forming the two-component mixture. Consequently, it does not follow a strict rule, but must be conducted empirically in order to take the gradient pt_(HB) into consideration in the best way possible.

Once the calculation of the gradient pt_(HB) has been conducted by the controller 22, the different variables of the oxygen/hydrogen gaseous mixture are provided by mathematical functions to be adapted as a function of the working conditions of the sensor according to the invention. These functions are quite complex, depending on whether the gas to be measured is hydrogen in oxygen or vice versa, or depending on the range of pressure of the gaseous mixture. In fact, hydrogen has a much higher thermal conductivity than oxygen. As a result of this, the high stable temperature T_(H) is lower in the case of a gaseous mixture formed substantially of hydrogen than in the case of a gaseous mixture formed mainly of oxygen. The difference between T_(H) and T_(B) is therefore smaller and the accuracy of the measurement is therefore lower. On the other hand, a broad working pressure range causes greater variations in behaviour of the gaseous mixture than a low pressure range, and this must be taken into account in the calculation of the variables of the gaseous mixture.

In the following description, two mathematical functions are proposed that allow determination of the composition of the gaseous mixture respectively in a simple case and in a more complex case in point. The first case corresponds, for example, to a pressure range of 1 to 5 bar. The second case in point applies, for example, to the detection of a low quantity of oxygen in hydrogen over a pressure range of 1 to 20 bar. It is to be understood that not all the working conditions of the gas sensor according to the invention will be explained in full detail in this description, but the mathematical functions given below can be adapted and modified to correspond to multiple conditions of use of the gas sensor without departing from the framework of the invention.

A first example of working condition relates to the measurement of a concentration of hydrogen ranging from 0 to 2 percent in oxygen over a pressure range varying from 0 to 5 bar. It has been determined by different calculations and tests that the pressure P and the proportion of hydrogen % H can be precisely represented by the following respective functions:

P=a*T _(H) +b*T _(H) ² +c*pt _(HB) +d*pt _(HB) ² +e*(T _(H) /pt _(HB))+f  (4)

% H=A*T _(H) +B*T _(H) ² +C*pt _(HB) +D*pt _(HB) ² +E*(T _(H) /pt _(HB))+F  (5)

in which coefficients a, b, c, d, e, f and A, B, C, D, E, F are characteristic of the gas sensor and are determined by a calibration procedure. Said calibration consists of measuring values T_(H) and pt_(HB) for three different pressure ranges and two different concentrations of hydrogen in the ranges of pressure and working hydrogen concentration, then by means of a solver minimising the differences between the measured and calculated values of P and % H. Equations (4) and (5) thus respectively deliver a hydrogen percentage value with an accuracy of 500 ppm and a pressure value with an accuracy of 0.2 bar.

A second example of working condition relates to the measurement of a concentration of oxygen ranging from 0 to 1 percent in hydrogen over a pressure range varying from 0 to 20 bar. In this case, the pressure P and the proportion of oxygen % O can be precisely represented by the following respective functions:

P=g*T _(H) +h*T _(H) ² +i*pt _(HB) +j*pt _(HB) ² +k*(T _(H) /pt _(HB))+1  (6)

% O=G*T _(H) +H*pt _(HB) +I*pt _(HB) ² +J*(T _(H) /pt _(HB))+K*(T _(A) −T _(ref))*(P−P _(ref))+L*(T _(A) −T _(ref))*(P−P _(ref))+M  (7)

in which coefficients g, h, i, j, k, l and G, H, I, J, K, L, M are determined as above, T_(A) is the ambient temperature measured by the measuring devices 15, T_(ref) is the reference temperature at which the calibration points are conducted and P_(ref) is the reference pressure at which the variation of resistance R_(M) is measured as a function of the temperature. This approach allows the effects of the ambient temperature T_(A) to be taken into account on the dependence curves of the conductivity of the gas as a function of pressure. This is second-order correction of the temperature. It also takes into account the effects of pressure on the temperature dependence of the measurement resistances 14 and 15. The thus improved equation (7) delivers a value of the proportion of hydrogen with an accuracy of 600 ppm over the entire range of working pressure and the pressure is given by equation (6) with an accuracy of 0.5 bar.

A thermal gas sensor for determining a concentration of gas in a two-component mixture at variable pressure has thus been described. It is understood that the gas sensor according to the invention is not restricted to the embodiments that have just been described and various simple modifications and variants can be envisaged by the person skilled in the art without departing from the framework of the invention as defined in the attached claims.

In particular, the parameters used by the gas sensor according to the invention are the high stable temperature T_(H) and the cooling gradient pt_(HB). In a particular context, a person skilled in the art could have cause to choose other parameters such as the high stable temperature T_(H) and the gradient for reheating the membrane pt_(BH) without involving inventive activity. The mathematical functions delivering the variables of the system from measured parameters would thus be potentially significantly different from the functions explained above.

It must also be mentioned that other means for heating the membrane 12 or for measuring its temperature are part of the framework of the present invention. For example, it is known that the temperature of a membrane immersed in a gas to be analysed can be delivered by a diode rather than by a metal line with thermo-variable resistance. Moreover, it is conceivable that another element of low thermal inertia such as a filament can be used in place of a membrane.

Finally, it is noted that the present invention relates to a method for determining the concentration of a gas in a two-component mixture at variable pressure. Said method is based on the measurement of a parameter in stable mode and a parameter in transient mode of the gaseous mixture and on the determination of a mathematical function to calculate the variables of the gaseous mixture from these parameters. A gas sensor has been described above that is particularly well suited to measuring these values and for application of this method. However, the method according to the invention is not restricted to such a sensor, but can be extended to any sensor that delivers the above-mentioned measurements by any appropriate means. 

What is claimed is:
 1. A sensor for determining the concentration of a gas in a two-component mixture at variable pressure, comprising: a measurement cell intended to be located in the two-component mixture, comprising a membrane of low thermal inertia, on which heating means for said membrane and measuring means that supplies a signal representative of the temperature T_(M) of said membrane are arranged side by side, a source of alternating current of frequency f intended to supply said heating means and an electronic circuit, wherein said frequency f is selected to enable the heating means to heat and alternately allow said membrane to be cooled so that its temperature T_(M) passes from a first stable value to a second stable value and vice versa via a transient mode, and that the electronic circuit is arranged to measure said signal to extract therefrom a first and a second parameter respectively relating to said first stable value and to the transient mode, and to calculate a value of the concentration of said gas and of the pressure of said two-component mixture from these parameters with the assistance of a previously established mathematical function and characteristic coefficients of said sensor.
 2. The sensor according to claim 1, wherein said first and second stable values are respectively a high stable temperature T_(H) of said membrane and a low stable temperature T_(B), and that said transient mode is a transient cooling mode t_(HB) of said membrane.
 3. The sensor according to claim 2, wherein said first parameter is representative of said high stable temperature T_(H) and said second parameter is representative of the rate of cooling of said membrane pt_(HB) during said transient cooling mode.
 4. The sensor according to claim 3, wherein the cooling rate of the membrane pt_(HB) is given by the following function: pt _(HB) =d/dt(In((T _(H) −T _(B))/(T _(i) −T _(B))) in which the points T_(i) are chosen at different intervals during the transient cooling mode t_(HB) of said membrane.
 5. The sensor according to claim 4, wherein the concentration of a gas of said two-component mixture is a polynomial function of said parameters representative of the high stable temperature T_(H) and the cooling rate pt_(HB) of the following type: A*T_(H)+B*T_(H) ²+C*pt_(HB)+D*pt_(HB) ²+E*(T_(H)/pt_(HB))+F in which A, B, C, D, E and F are included in said characteristic coefficients of the sensor and are obtained by calibration of said sensor.
 6. The sensor according to claim 4, wherein the pressure of said two-component mixture is a polynomial function of said parameters representative of the high stable temperature T_(H) and the cooling rate pt_(HB) of the following type: a*T_(H)+b*T_(H) ²+c*pt_(HB)+d*pt_(HB) ²+e*(T_(H)/pt_(HB))+f in which a, b, c, d, e and f are included in said characteristic coefficients of the sensor and are obtained by calibration of said sensor.
 7. The sensor according to claim 4, wherein the concentration of a gas of said two-component mixture is a polynomial function of said parameters representative of the high stable temperature T_(H), of the cooling rate pt_(HB), of the ambient temperature T_(A), of a reference temperature T_(ref) and of a reference pressure P_(ref) of the following type: G*T_(H)+H*pt_(HB)+I*pt_(HB) ²+J*(T_(H)/pt_(HB))+K*(T_(A)−T_(ref))*(P−P_(ref))+L*(T_(A)−T_(ref))*(P−P_(ref))²+M in which G, H, I, J, K, L and M are included in said characteristic coefficients of the sensor and are obtained by calibration of said sensor, and in which T_(ref) is the reference temperature at which the calibration is conducted and P_(ref) is the reference pressure at which said signal is calibrated as a function of the temperature of the membrane.
 8. The sensor according to claim 1, wherein it additionally comprises measuring devices that supply a signal representative of the ambient temperature T_(A) of the gaseous mixture, and that said signal representative of the temperature of the membrane is firstly corrected from the signal representative of the ambient temperature.
 9. A method for determining the concentration of a gas in a two-component mixture at variable pressure by means of a gas sensor comprising: a step of measuring a first characteristic parameter of the conduction of said two-component mixture, a step of measuring a second characteristic parameter of the diffusivity of said two-component mixture and a step of calculating a value of the concentration of said gas and the pressure of said two-component mixture from said parameters with the assistance of a previously established mathematical function and characteristic coefficients of said sensor.
 10. The method according to claim 9, wherein said first and second parameters are measured in alternating mode at a frequency f and are respectively representative of a high temperature T_(H) of an element of the sensor in stable mode and a cooling rate pt_(HB) of an element of the sensor in transient cooling mode t_(HB).
 11. The method according to claim 10, wherein said cooling rate pt_(HB) of an element of the sensor is given by the following function: pt _(HB) =d/dt(In((T _(H) −T _(B))/(T _(i) −T _(B))) in which the points T_(i) are measured at different intervals during the transient cooling mode t_(HB) of said sensor.
 12. A method according to claim 11, wherein the concentration of a gas of said two-component mixture is a polynomial function of said parameters representative of the high stable temperature T_(H) and the cooling rate pt_(HB) of the following type: A*T_(H)+B*T_(H) ²+C*pt_(HB)+D*pt_(HB) ²+E*(T_(H)/pt_(HB))+F in which A, B, C, D, E and F are included in said characteristic coefficients of the sensor and are obtained by calibration of said sensor.
 13. The method according to claim 11, wherein the pressure of said two-component mixture is a polynomial function of said parameters representative of the high stable temperature T_(H) and the cooling rate pt_(HB) of the following type: a*T_(H)+b*T_(H) ²+c*pt_(HB)+d*pt_(HB) ²+e*(T_(H)/pt_(HB))+f in which a, b, c, d, e and f are included in said characteristic coefficients of the sensor and are obtained by calibration of said sensor.
 14. The method according to claim 11, wherein the concentration of a gas of said two-component mixture is a polynomial function of said parameters representative of the high stable temperature T_(H), of the cooling rate pt_(HB), of the ambient temperature T_(A), of a reference temperature T_(ref) and of a reference pressure P_(ref) of the following type: G*T_(H)+H*pt_(HB)+I*pt_(HB) ²+J*(T_(H)/pt_(HB))+K*(T_(A)−T_(ref))*(P−P_(ref))+L*(T_(A)−T_(ref))*(P−P_(ref))²+M in which G, H, I, J, K, L and M are included in said characteristic coefficients of the sensor and are obtained by calibration of said sensor, and in which T_(ref) is the reference temperature at which the calibration is conducted and P_(ref) is the reference pressure at which said signal is calibrated as a function of the temperature of the membrane. 